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These ciffereut explanations may be discutaneled by appealing to mid-IR data (sec.e.g..son&IIoldeu2010:Salimetal. 2009).
These different explanations may be disentangled by appealing to mid-IR data \citep[see, e.g.,][]{kh10,sa09}.
Taking our results at face value. we iuter that stellar masses and other stellar population parameters derived using the Maraston(2005) imüght be biased for certain evolutionary phases;
Taking our results at face value, we infer that stellar masses and other stellar population parameters derived using the \cite{ma05} might be biased for certain evolutionary phases.
We stress that our fudiuss do not imply that the Druzual&Charlot(2003) models are best for all galaxies or for all evolutionary phases.
We stress that our findings do not imply that the \cite{bc03} models are best for all galaxies or for all evolutionary phases.
Using similar techniques as preseuted im this Letter. in combination with flexible SPS models which allow unrestricted. modification of uncertain evolution. plascs and input parameters (such as metallicity). it wall be possible to substautially reduce many of the major uncertainties plaguing all SPS models.
Using similar techniques as presented in this Letter, in combination with flexible SPS models, which allow unrestricted modification of uncertain evolution phases and input parameters (such as metallicity), it will be possible to substantially reduce many of the major uncertainties plaguing all SPS models.
We thank the referee for a verv constructive report. Jenny (ποσο, James Camu. and Scott Trager for useful discussions. and the COSMOS and AEGIS teams for the release of lagh-quality iiultiwaveleusth data sets to the conimnuiunuitv.
We thank the referee for a very constructive report, Jenny Greene, James Gunn, and Scott Trager for useful discussions, and the COSMOS and AEGIS teams for the release of high-quality multi-wavelength data sets to the community.
half the (spectroscopically determined) stellar rotation period.
half the (spectroscopically determined) stellar rotation period.
They argue that this may indicate the existence of resonant interactions between the planet’s orbit and its rotating host star. the absence of such resonances in systems containing cooler stars suggesting that Jupiter-mass planets can only interact effectively with stars with very shallow outer convective zones.
They argue that this may indicate the existence of resonant interactions between the planet's orbit and its rotating host star, the absence of such resonances in systems containing cooler stars suggesting that Jupiter-mass planets can only interact effectively with stars with very shallow outer convective zones.
Similarly. if some other factor brought the CoRoT-Exo- system to the I:] ratio between stellar rotation and orbital period that is observed today. resonant interaction between star and planet may have maintained this ratio thereafter.
Similarly, if some other factor brought the CoRoT-Exo-4 system to the 1:1 ratio between stellar rotation and orbital period that is observed today, resonant interaction between star and planet may have maintained this ratio thereafter.
Any subsequent evolution of the star’s rotation rate is likely to have been modest: (seee.g.Fig.1of?)..
Any subsequent evolution of the star's rotation rate is likely to have been modest: \citep[see e.g. Fig.~1 of][]{bar03}.
acceleration of CMESs ceases near (he peak (ime of the soft X-ray Mares.
acceleration of CMEs ceases near the peak time of the soft X-ray flares.
The final phase is a propagation al a constant or slowly decreasing speed.
The final phase is a propagation at a constant or slowly decreasing speed.
This temporal correlation between the CME velocity and the soft X-ray flux of the flare is frther confirmed in CMESs characterized by intermediate ancl gradual acceleration (Zhangetal.2004).
This temporal correlation between the CME velocity and the soft X-ray flux of the flare is further confirmed in CMEs characterized by intermediate and gradual acceleration \citep{zhang04}.
. CAIEs in our observations. however. feature a quasi-static inflation phase of the coronal arcade al <5 for about 412 hrs. followed apparently bv a similar three-phase paradigm as established by Zhangetal.(2001.2004).. during which the arcade evolves into the CME front.
CMEs in our observations, however, feature a quasi-static inflation phase of the coronal arcade at $<$ for about 4–12 hrs, followed apparently by a similar three-phase paradigm as established by \citet{zhang01,zhang04}, during which the arcade evolves into the CME front.
The gradual inflation of both PEAs ancl OAs seems to be a response of coronal magnetic fields to the continued injection of magnetic free energy [rom below. via παν enmiergence. or photospheric flows. as demonstrated by the increasing helicity accumulation prior to the eruption.
The gradual inflation of both PEAs and OAs seems to be a response of coronal magnetic fields to the continued injection of magnetic free energy from below, via flux emergence, or photospheric flows, as demonstrated by the increasing helicity accumulation prior to the eruption.
One may argue that for PEA events the preceding eruption might nol release all of the free energy. available. which makes the subsequent eruption possible.
One may argue that for PEA events the preceding eruption might not release all of the free energy available, which makes the subsequent eruption possible.
llowever. since the quasi-static stage lasts for hours. during which the PEA sometimes survives multiple flares. we suppose that the arcade is quite stable. otherwise. a little additional enereyv supply or disturbance might have triggered its eruption.
However, since the quasi-static stage lasts for hours, during which the PEA sometimes survives multiple flares, we suppose that the arcade is quite stable, otherwise, a little additional energy supply or disturbance might have triggered its eruption.
Therefore. it is reasonable io assume that a sienilicant portion of the energv powering the eruption of the PEA is accumulated curing (he quasi-static stage.
Therefore, it is reasonable to assume that a significant portion of the energy powering the eruption of the PEA is accumulated during the quasi-static stage.
Ii general. the (nmescale of (he quasi-static stage is dependent on both the stabilitv of the pre-CME structure and the accumulation rate of mmagnelic [ree energy in the corona.
In general, the timescale of the quasi-static stage is dependent on both the stability of the pre-CME structure and the accumulation rate of magnetic free energy in the corona.
There may exist a distribution of the Gimescale spanning from hours (for the events studied in this paper) to days (for helmet streamers).
There may exist a distribution of the timescale spanning from hours (for the events studied in this paper) to days (for helmet streamers).
For example. Sheelev&Wang(2007) observed the eracdual inflation of much hisher coronal loops in the LASCO ΕΟΝ. which sustains for |2 davs at and ends with the sudden formation of a pair of inward and outward components moving at speeds of and respectively.
For example, \citet{sw07} observed the gradual inflation of much higher coronal loops in the LASCO FOV, which sustains for 1–2 days at and ends with the sudden formation of a pair of inward and outward components moving at speeds of and, respectively.
Nevertheless. we suppose that a quasi-static stage. which corresponds io the enerev accumulation in the corona. is inherent to the kinetic evolution of any CME. no matter if the pre-CME structure has the right temperature and density {ο be seen in a narrow filter like EIT 195A.
Nevertheless, we suppose that a quasi-static stage, which corresponds to the energy accumulation in the corona, is inherent to the kinetic evolution of any CME, no matter if the pre-CME structure has the right temperature and density to be seen in a narrow filter like EIT 195.
While it is generally agreed (hat the [free οποιον powering CMESs is most Likely stored in stressed. ((wisted or sheared) fields. there has been contentious debate over the nature of the pre-eruption configuration.
While it is generally agreed that the free energy powering CMEs is most likely stored in stressed (twisted or sheared) fields, there has been contentious debate over the nature of the pre-eruption configuration.
The debate focuses on two competing models. namely. fux rope models vs. sheared-arcade models.
The debate focuses on two competing models, namely, flux rope models vs. sheared-arcade models.
In the sheared-arcade models. a flux rope is formed via magnetic reconnection during the course of the eruption (e.g..Antiochosetal.1999).
In the sheared-arcade models, a flux rope is formed via magnetic reconnection during the course of the eruption \citep[e.g.,][]{adk99}.
. ]lence it has been argued Chat a pre-existent Πας rope is unnecessary for solar eruptions.
Hence it has been argued that a pre-existent flux rope is unnecessary for solar eruptions.
On
On
An important property of scalar matrices ts that they have the same representation in all coordinate systems. so is defined independently of coordinate frame.
An important property of scalar matrices is that they have the same representation in all coordinate systems, so is defined independently of coordinate frame.
Diagonal matrices correspond to effects that affect the two e components independently. without intermixing.
Diagonal matrices correspond to effects that affect the two $\vec e$ components independently, without intermixing.
. Note that unlike scalarness. diagonality depend on choice of coordinate systems.
Note that unlike scalarness, diagonality depend on choice of coordinate systems.
For example. if we consider linear dipoles. their electronic. gains are (nominally) independent. and the corresponding Jones matrix is diagonal in an xy coordinate basis: The gains of a pair of circular receptors. on the other hand. are not diagonal in an vy frame (but are diagonal in a circular polarization frame — see Sect. 6.3)).
For example, if we consider linear dipoles, their electronic gains are (nominally) independent, and the corresponding Jones matrix is diagonal in an $xy$ coordinate basis: The gains of a pair of circular receptors, on the other hand, are not diagonal in an $xy$ frame (but are diagonal in a circular polarization frame – see Sect. \ref{sec:circular}) ).
Matrices with non-zero off-diagonal terms intermix the two components of e.
Matrices with non-zero off-diagonal terms intermix the two components of $\vec e$.
A special case of this is the matrix: Like diagonality. the property of being a rotation matrix also depends on choice of coordinate frame.
A special case of this is the matrix: Like diagonality, the property of being a rotation matrix also depends on choice of coordinate frame.
Examples of rotation matrices (in. an av frame) are rotation through parallactic angle P. and Faraday rotation in the tonosphere PF.
Examples of rotation matrices (in an $xy$ frame) are rotation through parallactic angle $\jones{P}{}$ , and Faraday rotation in the ionosphere $\jones{F}{}$.
Note also that rotation in an xy frame becomes a special kind of diagonal matrix in the circular frame (see Sect. 6.3)).
Note also that rotation in an $xy$ frame becomes a special kind of diagonal matrix in the circular frame (see Sect. \ref{sec:circular}) ).
It is important for our purposes that. while in general matrix multiplication is non-commutative. specific kinds of matrices do commute: Rules 2 and 3 are not very satisfactory às stated. because "diagonal" and "rotation" are properties defined in a specific coordinate frame. while (non-)commutation is defined independently of coordinates: two linear operators A and B either commute or they don’t. so their matrix representations must necessarily commute (or not) irrespective of what they look like for a particular basis.
It is important for our purposes that, while in general matrix multiplication is non-commutative, specific kinds of matrices do commute: Rules 2 and 3 are not very satisfactory as stated, because “diagonal” and “rotation” are properties defined in a specific coordinate frame, while (non-)commutation is defined independently of coordinates: two linear operators $\jones{A}{}$ and $\jones{B}{}$ either commute or they don't, so their matrix representations must necessarily commute (or not) irrespective of what they look like for a particular basis.
Let us adopt a practical generalization: if there exists a coordinate basis in which A and B are both diagonal (or both a )). then AB=BA in all coordinate frames.
Let us adopt a practical generalization: if there exists a coordinate basis in which $\jones{A}{}$ and $\jones{B}{}$ are both diagonal (or both a ), then $\jones{A}{} \jones{B}{}=\jones{B}{}\jones{A}{}$ in all coordinate frames.
We shall be making use of commutation properties later on.
We shall be making use of commutation properties later on.
Equation (8)) is universal in the sense that the J, and J, terms represent all effects along the signal path rolled up into one 2x matrix.
Equation \ref{eq:me0}) ) is universal in the sense that the $\jones{J}{p}$ and $\jones{J}{q}$ terms represent all effects along the signal path rolled up into one $2\times2$ matrix.
It is time to examine these in more detail.
It is time to examine these in more detail.
In the ideal case of a completely uncorrupted observation. there is one fundamental effect remaining — that of phase delay associated with signal propagation.
In the ideal case of a completely uncorrupted observation, there is one fundamental effect remaining – that of phase delay associated with signal propagation.
We are not interested in absolute phase. since the averaging operator implicit in a correlation measurement such as Eq. (3))
We are not interested in absolute phase, since the averaging operator implicit in a correlation measurement such as Eq. \ref{eq:correlation}) )
is only sensitive to phase between voltages v, and vy.
is only sensitive to phase between voltages $\vec v_p$ and $\vec v_q$.
Phase difference is due to the geometric pathlength difference from source to antennas p and q.
Phase difference is due to the geometric pathlength difference from source to antennas $p$ and $q$.
For reasons discussed in Sect. 5.2..
For reasons discussed in Sect. \ref{sec:smearing},
we want to minimize this difference for a specific direction. so a correlator will usually introduce additional delay terms to compensate for the pathlength difference in the chosen direction. effectively “steering” the interferometer.
we want to minimize this difference for a specific direction, so a correlator will usually introduce additional delay terms to compensate for the pathlength difference in the chosen direction, effectively “steering” the interferometer.
This direction ts called thecentre.
This direction is called the.
The conventional approach is to consider phase differences on pq. but for our purposes lets pick an arbitrary zero point. and consider the phase difference at eachantenna p relative to the zero point.
The conventional approach is to consider phase differences on $pq$, but for our purposes let's pick an arbitrary zero point, and consider the phase difference at eachantenna $p$ relative to the zero point.
Let usadopt the conventional coordinate and notations (seee.g.2). with the z axis pointing towards the phase centre. and consider antenna p located at coordinates Uy=(tp.Vp.Wp).
Let usadopt the conventional coordinate and notations \citep[see e.g.][]{tms}, with the $z$ axis pointing towards the phase centre, and consider antenna $p$ located at coordinates $\vec u_p=(u_p,v_p,w_p)$.
The phase difference at point uj relative to u=0. fora signal arriving from direction σ. is given by where /.n.n=VI—£np are the direction cosines of σσ. and Jt is signal wavelength.
The phase difference at point $\vec u_p$ relative to $\vec u=0$, for a signal arriving from direction $\vec\sigma$, is given by where $l,m,n=\sqrt{1-l^2-m^2}$ are the direction cosines of $\vec\sigma$, and $\lambda$ is signal wavelength.
It is customary to define z 1n units of wavelength. which allows us to omit the 4! term.
It is customary to define $\vec u$ in units of wavelength, which allows us to omit the $\lambda^{-1}$ term.
Following ?.. Lean now introduce a scalar matrix representing the phase delay effect.
Following \citet{JEN:note185}, I can now introduce a scalar matrix representing the phase delay effect.
After all. phase delay is just another linear transformation ofthe signal. and is perfectly amenable to the Jones formalism: The RIME for a single uncorrupted point source is then simply: Substituting the exponents for Κ from Eq. (10).
After all, phase delay is just another linear transformation ofthe signal, and is perfectly amenable to the Jones formalism: The RIME for a single uncorrupted point source is then simply: Substituting the exponents for $K_p$ from Eq. \ref{eq:K}) ),
and remembering that scalar matrices commute with everything. we canrecast Eq. (119)
and remembering that scalar matrices commute with everything, we canrecast Eq. \ref{eq:me-point-source}) )
in a more traditional which expresses the visibility as a function. of t.
in a more traditional which expresses the visibility as a function of $\vec u_{pq}$ .
1 shall call the visibility matrix given by Eqs. CH)
I shall call the visibility matrix given by Eqs. \ref{eq:me-point-source}) )
or (12)) the coherency. and write it as
or \ref{eq:me-point-source-uvw}) ) the , and write it as
PN.
PN.
It is expected that the brightest PN come from a slightly metal poor population (Ciarcdullo Jacoby 1992]) as predicted by the models of Dopita et al (1992)).
It is expected that the brightest PN come from a slightly metal poor population (Ciardullo Jacoby \cite{cija}) ) as predicted by the models of Dopita et al \cite{djv}) ).
In this contest it would be useful to search for Galactic bulge PN with super-solay mctallicity in order to reach a clearer understaudius of the role of metallicty ou PN evolution.
In this context it would be useful to search for Galactic bulge PN with super-solar metallicity in order to reach a clearer understanding of the role of metallicty on PN evolution.
lu acedlition more aix better data on the PN aud the stellar populations in netal rich svsteius. not coufined to the bulees of spirals. are required for an wuderstanding of what controls PN evolution in such cuviromments before detailed evolutionary scenerios m particular galaxies cau be developed.
In addition more and better data on the PN and the stellar populations in metal rich systems, not confined to the bulges of spirals, are required for an understanding of what controls PN evolution in such environments before detailed evolutionary scenerios in particular galaxies can be developed.
Tn order for the PN to be reliable tracers. their abundanuces luust reflect those of the easons from. which the stars were formed and not solely be a consequence of nuclear reprocessing.
In order for the PN to be reliable tracers, their abundances must reflect those of the gas from which the stars were formed and not solely be a consequence of nuclear reprocessing.
From studies of Galactic PN. the O. Ne. S and Ar eradieut (Maciel Kopppen 1991)) matches that of the ITIIT regions (Shaver ot al. 1983))
From studies of Galactic PN, the O, Ne, S and Ar gradient (Maciel Köpppen \cite{mac}) ) matches that of the II regions (Shaver et al. \cite{shav}) )
as does the He eracient (Peinibert Serrano 1980)).
as does the He gradient (Peimbert Serrano \cite{pei}) ).
This applies to the (common) Type II rebulac. not to the minority Type E PN. originating from Helier ass progenitors and having euhanced Te. N and Ne.
This applies to the (common) Type II nebulae, not to the minority Type I PN, originating from higher mass progenitors and having enhanced He, N and Ne.
The Type II PN and ITT regions iu the lower uetallicitv cuviroument of the Magellanic Clouds also indicate siuular abundances (see Cleeeee 1993)).
The Type II PN and II regions in the lower metallicity environment of the Magellanic Clouds also indicate similar abundances (see Clegg \cite{cleg}) ).
Richer (1993]) las arrived at the iuportaut couclusion that he brightest PN in cllipticals have the same status as abundance indicators as TTT reeious iu spirals.
Richer \cite{rich}) ) has arrived at the important conclusion that the brightest PN in ellipticals have the same status as abundance indicators as II regions in spirals.
Spectra comparable to or better than the ones presented here for PN#11902. 1001 and 5601 are require to distinguish the Type HI roni Type I nebulae aud to determine improved oxveen abuudances.
Spectra comparable to or better than the ones presented here for 1902, 4001 and 5601 are required to distinguish the Type II from Type I nebulae and to determine improved oxygen abundances.
For the brighest PN it will be feasible to detect the ο iue and thus determine O abundauces to £0.2dex or better: for lower luminosity PN. or galaxies more distaut than NGC 5128. empirical abundance determination aud photoionization modclling. as performed here. is required aud the derived abundances are of lower individual weight.
For the brighest PN it will be feasible to detect the [O line and thus determine O abundances to $\pm$ 0.2dex or better; for lower luminosity PN, or galaxies more distant than NGC 5128, empirical abundance determination and photoionization modelling, as performed here, is required and the derived abundances are of lower individual weight.
However average oxvgen abunudances at least comparable in accuracy to those for the integrated stellar population asa function of radius. aud for individual elobular clusters. are achievable.
However average oxygen abundances at least comparable in accuracy to those for the integrated stellar population as a function of radius, and for individual globular clusters, are achievable.
A rather large sample of PN is required to distinguish a trend in the abundance. since a PN at a giveu effective radius may reside at a large distance frou he ealaxy. due to projection.
A rather large sample of PN is required to distinguish a trend in the abundance, since a PN at a given effective radius may reside at a large distance from the galaxy, due to projection.
The racial velocity data could be used to eive a partial answer to distinguish halo PN ποια body PN.
The radial velocity data could be used to give a partial answer to distinguish halo PN from body PN.
Multi-object spectroscopy techniques are required to obtain spectra of the requisite nmuubers of PN to distinenish a trend aud to sample the lime of sieht abuudance spread. excludiug halo objects.
Multi-object spectroscopy techniques are required to obtain spectra of the requisite numbers of PN to distinguish a trend and to sample the line of sight abundance spread, excluding halo objects.
Towever eiven that most of the PN are projected against a strong stellar coutinuuim. then ulti-sht rather than 1inulti-Bbre iustrunents are required to provide accurate backeround subtraction of the spectra.
However given that most of the PN are projected against a strong stellar continuum, then multi-slit rather than multi-fibre instruments are required to provide accurate background subtraction of the spectra.
Coherent fibre bundles. one for cach PN. could alternatively be employed to allow effective 2-D backeround subtraction.
Coherent fibre bundles, one for each PN, could alternatively be employed to allow effective 2-D background subtraction.
Ποπονα single fibres are adequate for radial velocity work based on the brightest ine of5007A.
However single fibres are adequate for radial velocity work based on the brightest line of.
. Since the orientation of a slit must be kept fixed to provide a good background subtraction and to allow several PN to be observed per slit. then the use of an Atinospheric Dispersion Corrector is highly advantageous oO ensure spectrophotometry over the requisite large wavelength rauge (~3700 - ‘for Πο, N. O. Ne and S abundance determinations).
Since the orientation of a slit must be kept fixed to provide a good background subtraction and to allow several PN to be observed per slit, then the use of an Atmospheric Dispersion Corrector is highly advantageous to ensure spectrophotometry over the requisite large wavelength range $\sim$ 3700 - for He, N, O, Ne and S abundance determinations).
When considering observation of PN in galaxies more distaut han NGC 5128. the issue of background subtraction will become more crucial as lavecr variations m galaxy continuni will be included iu the slit or aperture.
When considering observation of PN in galaxies more distant than NGC 5128, the issue of background subtraction will become more crucial as larger variations in galaxy continuum will be included in the slit or aperture.
Spectrophotometry of extra-galactic PN is a field where iulti-object techniques ou 8-101à telescopes will bring a rich harvest of data to bear on the history of chemical chrichiment iu galaxies of all types.
Spectrophotometry of extra-galactic PN is a field where multi-object techniques on 8-10m telescopes will bring a rich harvest of data to bear on the history of chemical enrichment in galaxies of all types.
The first spectra of planetary nebulae in the ucarby carly-ype galaxy NGC 5128 lave been presented.
The first spectra of planetary nebulae in the nearby early-type galaxy NGC 5128 have been presented.
The spectra of five PN from the catalogue of ITui ct al. (1993h))
The spectra of five PN from the catalogue of Hui et al. \cite{huib}) )
have sco. Observed over an observed emission Lue brightuess rage of a factor 8 and galactocentiic radius range from 7 o 18 kpe.
have been observed over an observed emission line brightness range of a factor 8 and galactocentric radius range from 7 to 18 kpc.
The spectra show characteristic high ionization enission lines similar to Galactic PN aud confirming that he brightest PN ina galaxy are eutirely typical.
The spectra show characteristic high ionization emission lines similar to Galactic PN and confirming that the brightest PN in a galaxy are entirely typical.
The mean O/T] of the five PN. determined by empirical methods and modelling. is 0.5 with a spread of O.3dex.
The mean [O/H] of the five PN, determined by empirical methods and modelling, is $-$ 0.5 with a spread of 0.3dex.
This low netallicity coutrasts with that of the assmued metal rich stellar population of NGC 5128.
This low metallicity contrasts with that of the assumed metal rich stellar population of NGC 5128.
Ihuris et al. (
Harris et al. (
AJ 116. 2866. 1998 and AJ 117. 855. 1999) have obtained IIST photometry of a globular cluster and the feld halo stars in NGC 5128. situated at a distance of ~21 kpe from the galaxy centre.
AJ 116, 2866, 1998 and AJ 117, 855, 1999) have obtained HST photometry of a globular cluster and the field halo stars in NGC 5128, situated at a distance of $\sim$ 21 kpc from the galaxy centre.
For the halo stars they estimate a dean metallicity of <[FefIT|> = 0.L but with a broad range.
For the halo stars they estimate a mean metallicity of $<[Fe/H]>$ = $-$ 0.4, but with a broad range.
Although he PN observed in this paper were at smaller galactocentrie distances. there is interesting agreenient between the metallicity of the PN from the [O/TI] determinations presented here and those for the Red Cdaut Brauch stars observed by Iuris et al.
Although the PN observed in this paper were at smaller galactocentric distances, there is interesting agreement between the metallicity of the PN from the [O/H] determinations presented here and those for the Red Giant Branch stars observed by Harris et al.
uncertainty of the fits, but remain significantly different from the trend predicted by Hartmann et al. (
uncertainty of the fits, but remain significantly different from the trend predicted by Hartmann et al. (
1998) and Muzerolle et al. (
1998) and Muzerolle et al. (
2000) for viscous disc evolution (solid lines).
2000) for viscous disc evolution (solid lines).
In principle, the shallower of our fits could be affected by our very strict criteria for slopesselecting bona-fide PMS stars.
In principle, the shallower slopes of our fits could be affected by our very strict criteria for selecting bona-fide PMS stars.
Requiring that the Ha excess be at the 4c level or higher and that Weg<—20 wwill set a lowerlimit to the Ha luminosity that we can accept as significant and, therefore, to the smallest Mace value that we can detect at a given mass or age.
Requiring that the $\alpha$ excess be at the $4\,\sigma$ level or higher and that $W_{\rm eq} < -20$ will set a lowerlimit to the $\alpha$ luminosity that we can accept as significant and, therefore, to the smallest $\dot M_{\rm acc}$ value that we can detect at a given mass or age.
If this lower limit is too high, we could be ignoring too many objects with low mass accretion rate, particularly at older ages, and therefore skew the measurement of the slope towards low values.
If this lower limit is too high, we could be ignoring too many objects with low mass accretion rate, particularly at older ages, and therefore skew the measurement of the slope towards low values.
On the other hand, it appears that our detection limits (shown by the thin short-dashed lines for the mass of each do not significantly affect the determinationaverage of the slope, group)except possibly for the least massive stars at ages >10 MMyr.
On the other hand, it appears that our detection limits (shown by the thin short-dashed lines for the average mass of each group) do not significantly affect the determination of the slope, except possibly for the least massive stars at ages $> 10$ Myr.
For this group, however, the slope is determined by the much more numerous stars.
For this group, however, the slope is determined by the much more numerous young stars.
More importantly,young the upper envelopes of the distribution of all four mass groups appear to be fully consistent with the slope of the best fit.
More importantly, the upper envelopes of the distribution of all four mass groups appear to be fully consistent with the slope of the best fit.
This is shown graphically by the thin long-dashed lines that represent the best-fitting line shifted vertically by 0.5 ddex.
This is shown graphically by the thin long-dashed lines that represent the best-fitting line shifted vertically by $0.5$ dex.
While our conservative limits on the Ha excess emissionmay prevent us from detecting objects with low L(Ho), no selection effects are to be expected for stars with high Ha luminosity.
While our conservative limits on the $\alpha$ excess emissionmay prevent us from detecting objects with low $L(H\alpha)$, no selection effects are to be expected for stars with high $\alpha$ luminosity.
Since the distribution of these objects is consistent with the slope of the best fit, the latter must be correct.
Since the distribution of these objects is consistent with the slope of the best fit, the latter must be correct.